Nuclear magnetic resonance (NMR) is used as a tool in a number of different technology areas to investigate different types of mediums. NMR can occur when the medium is subjected to a static magnetic field, B0, and to an oscillating magnetic field, B1. When subjected to an applied static magnetic field, polarization of nuclear magnetic spins of the medium occurs based on spin number of the medium and magnetic field strength. Applying an electromagnetic field to the medium in the static magnetic field can perturb the polarization established by the static magnetic field. In optimal measurements, the static magnetic field and the perturbing field are perpendicular to each other. Collected responses received from the medium related to the total magnetization of nuclear spins in the medium, in response to these applied fields, can be used to investigate properties of the medium, and may provide imaging of the medium. It is noted that magnetization is proportional to polarization.
Nuclear magnetic resonance measurements are created by the oscillation of excited nuclear magnetic spins in the transverse plane, that is, the direction perpendicular to the magnetic field. This oscillation eventually dies out and the equilibrium magnetization returns. The return process is referred to as longitudinal relaxation. The time constant, T1, for nuclei to return to their equilibrium magnetization, Mo, is called the longitudinal relaxation time or the spin lattice relaxation time. The magnetization dephasing, that is losing coherence, along the transverse plane is given by the time constant T2 and is called the spin-spin relaxation time. The loss of phase coherence can be caused by several factors including interactions between spins or magnetic gradients.
A widely used NMR measurement technique, designed by Carr, Purcell, Meiboom, and Gill and, hence, referred to as CPMG, uses a sequence of radio frequency pulses to produce spin echoes and counteract dephasing of the magnetization in the medium investigated. In the CPMG sequence, an initial pulse, commonly a 90° pulse, can be applied to tip the polarization into a plane perpendicular to the static magnetic field. To counter dephasing due to magnetic inhomogeneities, another pulse, a recovery pulse, commonly a 180° or other angle tipping pulse, is applied to return to phase, which produces a signal called an echo from the medium. Yet, after each return to phase, dephasing begins and another recovery pulse is applied for rephasing. Rephasing or refocusing is repeated many times in the CPMG sequence, while measuring each echo. The echo magnitude decreases with time due to a number of irreversible relaxation mechanisms. The CPMG sequence can have any number of echoes, where the time between each echo can be relatively short, for example, of the order of 1 ms or less or as long as 12 ms is used.
FIG. 1 illustrates use of a 90° tipping pulse and a sequence of 180° refocusing pulses. In this sequence, the ten 180° refocusing pulses cause ten echoes 107-1 . . . 107-10, where the peak amplitudes of the echoes are equally spaced apart by a peak to peak time distance, TE, that corresponds to the equally spaced apart time distances of the refocusing pulses. Also indicated are an acquisition window for capturing the signal of an echo, a first echo E1, a second echo E2, and A0. A0 is the amplitude of the echo train at time zero. A0 can be calculated by using an exponential decay fitting curve determined from a third echo E3 to the last echo. E1 and E2 can be included if they are corrected. These echoes decay according to the T2 of the medium. Once the nuclear spin population is fully recovered for the sequence, the medium can be probed again by another sequence.
Petrophysical information can be derived from NMR measurements, such as, but not limited to petrophysical properties of fluid containing porous media. Various properties that can be measured using an NMR logging tool include pore size, porosity, surface-to-volume ratio, formation permeability, and capillary pressure. For instance, the distribution of T2 values can be used to estimate pore size. As noted above, T2 is related to loss of phase coherence that occurs among spins, which can be caused by several factors. For example, magnetic field gradients in pores lead to different decay rates. Thereby different pore sizes in the formation produce a distribution of T2 values, which is shown in the conversion of spin-echo decay data of NMR measurements. This distribution represents a “most likely” distribution of T2 values that produce the echo train of the measurement. This distribution can be correlated with a pore size distribution when the rock is 100% water saturated. However, if hydrocarbons are present, the T2 distribution will be altered depending on the hydrocarbon type, viscosity, and saturation. With proper calibration and account for hydrogen index of the fluids in the pore space, the area under a T2 distribution curve is equal to total porosity. More precision in the evaluation of NMR data may be aided with increased acquisition of data from multiple NMR measurements.
A 90° pulse has the function of tipping the magnetization into the transverse plane, while a 180° pulse has the function of inverting the magnetization. A pulse has two characterizations: length in time, called duration, and amplitude. The pulse can be modulated by frequency and amplitude, which gives it a density. These two characterizations play off each other. A 90° pulse can be achieved by having the correct integrated amplitude. When a pulse intended to tip a sample 90° degrees has the wrong integration, it is no longer a true 90° pulse. When a pulse intended to tip a sample 90° degrees is not a true 90° pulse, the NMR signal is reduced. Therefore, in order to obtain the best signal-to-noise ratio (SNR), it is important that the intended 90° pulse has a correct shape, both in duration and density, to flip the magnetization by 90° degrees, as well as the intended 180° having a correct shape. Herein, pulses with certain intent that are not achieving their desired intent are designated by quotation marks. For example, “90” stands for a pulse which tips magnetization near 90° but not actually 90 degrees. Also, “180” stands for a pulse intending to be 180°, but the tipping angle is either larger or smaller than 180°. In general, the 180° pulse has twice the duration of the 90° pulse with the same amplitude. However, the 180° pulse need not be defined in this manner, and can be calibrated separately from a 90° pulse.
A current method of calibrating for optimal 90° flip in a magnetic resonance imaging logging tool can include running CPMG sequences as shown in FIGS. 2-5, in which amplitude is varied and the resulting A0 values or echo amplitudes are compared. Alternatively, variation of pulse duration can be used.
The CPMG sequence is followed by a wait time, WT. This wait time is usually about 5 times the T1 of the solution. In pure water, the WT can be on the order of 12 to 15 seconds. Usually water is doped, lowering T1, in the calibration tank, which can cause additional error and problems. Other substances, for example, glycerol and peanut oil, can be used to calibrate a tool.
In these calibration processes, correction for the first two echoes (E1 and E2) of the pulse train can also be found. A restriction on the calibration sample in these processes is that it has NMR active nuclei for the experiment. There are also limitations on how small the T2 can practically be. The hydrogen index of the calibration sample is also a useful piece of information.
The calibrations for the 90° and 180° pulses are performed iteratively in their respective current methods. Either the 90° calibration or the 180° calibration can be performed first. FIG. 2 shows a typical CPMG sequence for a conventional tool calibration in which an intended ninety degree amplitude is varied, while an intended one hundred eighty length and amplitude are held constant. A “180” pulse length and amplitude are chosen and held constant, while the “90” pulse is incremented through many different amplitudes. Having “90” pulse amplitudes varied, while “180” pulse amplitude is held constant provides a first stage. A best “90” from this first stage is then determined by determining the maximized A0 or echo amplitude. The best “90” may be determined by curve fitting to find the highest A0 or echo values. The determined best “90” pulse is then used in a sequence, where the “90” pulse properties are held constant and the “180” pulses are varied.
FIG. 3 shows a typical CPMG sequence for a conventional tool calibration in which an intended one hundred eighty amplitude is varied, while an intended ninety degree amplitude is held constant. Varying “180” pulse amplitude, while “90” pulse amplitude is held constant, provides a second stage to the procedure. A best “180” pulse is then determined by determining the maximized A0 or echo amplitude. The best “180” pulse may be determined by curve fitting to find the highest A0 or echo values. As noted above, stage 2 may be conducted to determine a best “90” pulse with stage 1 conducted to determine a best “180” pulse.
A few iterations of these sequences can be performed until the best “90” to “180” ratio is determined Then, an overall amplitude assessment can be conducted, where the sequence is scaled incrementally. FIG. 5 shows a typical calibration method that compares A0, E1, and E2 values, which are fit to 2-degree polynomials. The A0 values can be solved for the best amplitude (AM) or strength B1 of the CPMG pulse. This results in a determination of an overall amplitude to be used down hole. In addition, E1 and E2 correction factors can be calculated.